Good planarity and the minimization of interconnect thickness variation is the advantage provided by chemical-mechanical planarization (CMP). It is well known that post-CMP topography variation is strongly dependent on layout pattern. Inter-layer (ILD) CMP processes can be approximated using linear models empirically where the polish pressure is directly correlated with the contact area and therefore the layout density. Such models can be applied to the insertion of dummy features to achieve minimal pattern density variation and therefore reduced post-CMP topography variation. A typical modeling flow is shown in FIG. 3.
Some models based on the modification to ILD CMP stress model have been applied to shallow trench isolation (STI) polish, as shown in the density-to-topography example in FIG. 1. However, metal CMP and other selective CMP processes (STI, Poly Gate Polish) cannot be described by linear models because of the interaction between physical and chemical effects that span feature and equipment scales. A good example is the dishing and erosion in copper (Cu) that occurs in the CMP process, which is caused by locally mismatched reaction rates between different materials on the substrate surface and the slurry.
No analytical model exists, especially for general, complex design layouts where the efficiency and the memory requirements of the modeling algorithm are essential. Previous modeling based on physical models has been limited to linear models or to two-dimensional simple feature patterns. A linear Preston's equation is not sufficient to model heterogeneous material removal on a pattern substrate. This is especially true when the removal rate as determined by chemistry is simultaneously related to redistribution of slurry particle contact stress due to feature-scale topography changes. Models for feature-scale CMP are needed to capture the dishing and erosion effects, while incorporating the effect of chemical reactivity.
Analytical design tools, methodology and modeling are needed for predicting non-linear CMP process effects that are computationally efficient.